In recent years, there have been advanced in the miniaturization of piezoelectric filters including thin-film bulk acoustic wave piezoelectric resonators (BAW resonators) using thickness vibration of piezoelectric thin films or surface acoustic wave resonators (SAW resonators) using surface acoustic waves.
For example, Patent Document 1 discloses that each face of a substrate including a resonator is bonded to a lid having the same size as the substrate to achieve a smaller package. Patent Document 2 discloses a structure in which two substrates each including a resonator are spaced and held parallel to each other with a protrusion of a case.    Patent Document 1: Japanese Patent Publication No. 2004-503164    Patent Document 2: Japanese Unexamined Patent Application Publication No. 2002-43890
Trends toward miniaturization of cellular phones and the like including piezoelectric filters require a further reduction in the size of piezoelectric filters.
In the structure disclosed in Patent Document 1, however, the package cannot be smaller than the substrate. At least two resonators including a series resonator and a parallel resonator need to be formed on the same plane of the substrate. The formation of many resonators on the same plane limits a reduction in the size of the substrate. Since the series resonator and the parallel resonator are formed on the same plane, it is difficult to reduce or increase the weight separately for the series and parallel resonators by ion milling, sputtering, or the like. The arrangement of a plurality of resonators on a plane increases wiring resistance between the resonators, thus easily leading to degradation in filter properties. The use of a plurality of materials and vibrational modes of resonators results in the restriction of the materials and complexity of a process to increase cost. The lid for protecting the resonators disposed on the substrate increases the size of the package. Furthermore, costs of the material and processing of the lid are also required.
In the structure disclosed in Patent Document 2, stacking the two substrates results in a smaller area of the structure. However, surrounding the substrates by the case results in a larger area of the structure than the substrate. Furthermore, the substrates are spaced with the protrusion. Top and bottom openings of the case housing the substrates are sealed with lids, thus increasing the height (dimension in the thickness direction of the substrates).